Cryptography: The Mathematics of Secret Codes

密码学：密码的数学

• 批准号: 0099220
• 负责人: Janet Beissinger
• 金额: $ 39.81万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-09-01 至 2006-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0099220&HistoricalAwards=false
• 关键词: Cryptography; Mathematics; Secret; Codes

This project develops an 8-week middle-school mathematics module that introduces cryptography, the science of sending secret messages, while teaching and reinforcing the learning of related mathematical concepts. The topics range from the classical encryption systems and the historic context in which they were used through powerful modern encryption systems that provide secrecy in electronic messages today. The module also covers passwords and codes that correct errors in the transmission of information. Public awareness of the importance of cryptography is growing, as is the need to understand the issues involved. The study of cryptography provides an interesting context for students to apply traditional mathematical skills and concepts. Mathematical topics covered include percents, probability, functions, prime numbers, decimals, inverses and modular arithmetic. The main product is a middle-school student book, with accompanying teacher materials. A web site is being developed that supports the activities in this book. Abbreviated modules for Grades 3, 4 and 5 are also being developed, as well as an instructor's guide for adapting the materials for use in informal educational settings such as museums and after-school programs. The development of the module involves piloting and field-testing by experienced classroom teachers from diverse school communities and instructors of informal educational programs. Evaluation includes review by mathematicians and educators, as well as an investigation into the level of students' understanding of the topics studied.

该项目开发了一个为期 8 周的中学数学模块，介绍密码学（发送秘密消息的科学），同时教授和强化相关数学概念的学习。 主题涵盖经典加密系统以及通过强大的现代加密系统使用它们的历史背景，这些系统为当今的电子消息提供保密性。 该模块还涵盖了纠正信息传输错误的密码和代码。 公众对密码学重要性的认识不断增强，了解所涉及问题的需求也在不断增强。 密码学的研究为学生应用传统数学技能和概念提供了一个有趣的背景。 涵盖的数学主题包括百分比、概率、函数、素数、小数、逆和模算术。主要产品为中学生用书，并附有教师教材。 正在开发一个网站来支持本书中的活动。 还正在开发针对 3、4 和 5 年级的缩略模块，以及教师指南，用于调整材料以在博物馆和课外项目等非正式教育环境中使用。 该模块的开发涉及由来自不同学校社区的经验丰富的课堂教师和非正式教育项目的教师进行的试点和现场测试。 评估包括数学家和教育工作者的审查，以及对学生对所研究主题的理解水平的调查。